Cryptology ePrint Archive: Report 2007/348

A Framework for Efficient and Composable Oblivious Transfer

Chris Peikert and Vinod Vaikuntanathan and Brent Waters

Abstract: We propose a simple and general framework for constructing oblivious
transfer (OT) protocols that are \emph{efficient}, \emph{universally
composable}, and \emph{generally realizable} from a variety of
standard number-theoretic assumptions, including the decisional
Diffie-Hellman assumption, the quadratic residuosity assumption, and
\emph{worst-case} lattice assumptions.

Our OT protocols are round-optimal (one message each way), quite
efficient in computation and communication, and can use a single
common string for an unbounded number of executions. Furthermore, the
protocols can provide \emph{statistical} security to either the sender
or receiver, simply by changing the distribution of the common string.
For certain instantiations of the protocol, even a common
\emph{random} string suffices.

Our key technical contribution is a simple abstraction that we call a
\emph{dual-mode} cryptosystem. We implement dual-mode cryptosystems
by taking a unified view of several cryptosystems that have what we
call ``messy'' public keys, whose defining property is that a
ciphertext encrypted under such a key carries \emph{no information}
(statistically) about the encrypted message.

As a contribution of independent interest, we also provide a multi-bit
version of Regev's lattice-based cryptosystem (STOC 2005) whose time
and space efficiency are improved by a linear factor in the security
parameter $n$. The amortized encryption and decryption time is only
$\tilde{O}(n)$ bit operations per message bit, and the ciphertext
expansion can be made as small as a constant; the public key size and
underlying lattice assumption remain essentially the same.